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**preview**shows half of the first page. to view the full**1 pages of the document.**~ Statistics Lecture #5 ~

Introduction to Sampling and Confidence Intervals

09/10/19

o Preview: Statistical Sampling

o The goal is to make inferences about a big group of individuals or items, from what we

know about from a well-chosen sample group.

o Specifically to estimate a number we don’t know in that larger group, with one we do know

from the sample

o Be able to quantify the confidence you can have in those inferences.

o We have to understand this can only be done probabilistically.

o An Example

o We have 132 students currently enrolled in this class.

o Canvas tells us various things about students’ activity so we can see who is engaged and who

is not.

o Suppose we want to estimate the proportion of the class with over 100 “Page Views.”

o We might do that based on a sample of 30 students.

o Sensible Estimate?

o Statistical science is about how to mathematically quantify the goodness of this common

sense.

o How the sample is taken is critical to that process.

o Statistical Sampling is More than Common Sense

o It is a probabilistic endeavor.

o It tells us a lot about how sample statistics behave from sample to sample.

o Provided we know that the sample was taken probabilistically

o Language in Upcoming Reading

o Population: Larger collection of subjects/items that you are interested in understanding

something about

o Sample: Subject/items chosen to be measured or interviewed

▪ Chosen from population

o List of Individuals:

1

2

3

4

5

6

7

8

9

10

o Population Parameter: Number the describes the population

▪ E.g. true proportion of all UK students who would answer “yes”

o Sample Statistic: Number that describes the sample

▪ E.g. observed proportion in sample who answered “yes”

o Simple Random Sampling: A Non-Trivial Probabilistic Idea

o A simple random sample (SRS) of size n consists of n individuals chosen from the

population in such a way that every set of n individuals had the same chance of being chosen.

▪ Notice this did not say “a kinda unbiased sort of thing that we made sure was spread

out and representative and stuff like that. You know, random.”

• Much more precise than that.

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